Catherine A. Brown University of Pittsburgh
Four studies that address the teaching of rational number topics are reviewed and critiqued in this chapter. It is argued that although currently available research on teaching and learning provides some helpful information for answering questions related to the teaching of rational number topics in classrooms, more collaboration among researchers is necessary if we are to develop a comprehensive picture of the complex enterprise of classroom teaching. Suggestions for such collaborative efforts are made.
Research that specifically investigates the teaching of rational number is scarce. Although mathematics classrooms have been used as sites for research on teaching (see, e.g., Borko & Livingston, 1989), this seems to be because of a perception that mathematics classrooms are good sites for learning about teaching in general, rather than because of researchers' interest in understanding mathematics teaching specifically. Researchers' focus on what could be termed the more generic aspects of teaching has led to research results that provide information about generic teaching activities such as planning, classroom management and organization, and the structure of explanations, but this focus does not address issues related specifically to the mathematics taught. Even research on mathematics instruction carried out in collaboration with mathematics educators, such as the well-known Active Mathematics Teaching work of Good, Grouws, and Ebmeier ( 1983), does not directly address issues related to the teaching of specific mathematics content, even though it provides important information about mathematics lesson structure.
Research on teaching rational number concepts and procedures ideally should draw on what we have learned from the ongoing content analysis of